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Descriptive Properties of Spaces of Measures

Student: Novikov Lev

Supervisor: Vladimir Bogachev

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2018

The main goal of the paper is the search for some general properties of the measure space P(X), where the measures are defined on some arbitrary topological space X. We consider the results already available for locally compact separable spaces, made by Lange and Fell, and consider a more complicated case when the space of measures P(X) turns out to be not analytic. To do this, we will describe Borel sets for Polish spaces, in particular, with the help of Borel isomorphism we will translate the Borel structure (in fact, the set of Borel sets or the topology) of the Polish space of interest to the Borel structure generated by the usual topology in the Hilbert cube. The resulting structure will be defined on a metric separable space, which allows us to obtain some properties of measure spaces.

Full text (added June 4, 2018)

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